Quantum Theories, Misc

It is shown that the heuristic "derivation" of the Schrödinger equation in quantum mechanics textbooks can be turned into a real derivation by resorting to spacetime translation invariance and relativistic invariance.

The meaning of the wave function and its evolution are investigated. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function of an isolated system obeys the free Schrödinger equation due to the requirements of spacetime translation invariance and (...) relativistic invariance. Thirdly, we argue that the random discontinuous motion of particles may lead to a stochastic, nonlinear collapse evolution of the wave function. A discrete model of energy-conserved wavefunction collapse is proposed and shown consistent with existing experiments and our macroscopic experience. Besides, we also give a critical analysis of the de Broglie-Bohm theory, the many-worlds interpretation and other dynamical collapse theories, and briefly discuss the issues of unifying quantum mechanics and relativity. (shrink)

We investigate the meaning of the wave function by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. In a realistic interpretation, the wave function of a quantum system can be taken as a description of either a physical field or the ergodic motion of a particle. The essential difference (...) between a field and the ergodic motion of a particle lies in the property of simultaneity; a field exists throughout space simultaneously, whereas the ergodic motion of a particle exists throughout space in a time-divided way. If the wave function is a physical field, then the mass and charge density will be distributed in space simultaneously for a charged quantum system, and thus there will exist gravitational and electrostatic self-interactions of its wave function. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus the wave function cannot be a description of a physical field but a description of the ergodic motion of a particle. For the later there is only a localized particle with mass and charge at every instant, and thus there will not exist any self-interaction for the wave function. Which kind of ergodic motion of particles then? It is argued that the classical ergodic models, which assume continuous motion of particles, cannot be consistent with quantum mechanics. Based on the negative result, we suggest that the wave function is a description of the quantum motion of particles, which is random and discontinuous in nature. On this interpretation, the square of the absolute value of the wave function not only gives the probability of the particle being found in certain locations, but also gives the probability of the particle being there. We show that this new interpretation of the wave function provides a natural realistic alternative to the orthodox interpretation, and its implications for other realistic interpretations of quantum mechanics are also briefly discussed. (shrink)

In this article I raise a new problem for quantum mechanics, which I call the control problem. Like the measurement problem, the control problem places a fundamental constraint on quantum theories. The characteristic feature of the problem is its focus on state preparation. In particular, whereas the measurement problem turns on a premise about the completeness of the quantum state ('no hidden variables'), the control problem turns on a premise about our ability to prepare or control quantum states. After raising (...) the problem, I discuss some applications. I suggest that it provides a useful new lens through which to view existing theories or interpretations, in part because it draws attention to aspects of those theories that the measurement problem does not. I suggest that it also helps clarify the physical significance of the well-known no-go result—the no-cloning theorem—on which it is based. (shrink)

Quasi-set theory $\cal Q$ allows us to cope with certain collections of objects where the usual notion of identity is not applicable, in the sense that $x = x$ is not a formula, if $x$ is an arbitrary term. $\cal Q$ was partially motivated by the problem of non-individuality in quantum mechanics. In this paper I discuss the range of explanatory power of $\cal Q$ for quantum phenomena which demand some notion of indistinguishability among quantum objects. My main focus is (...) on the double-slit experiment, a major physical phenomenon which was never modeled from a quasi-set-theoretic point of view. The double-slit experiment strongly motivates the concept of degrees of indistinguishability within a field-theoretic approach, and that notion is simply missing in $\cal Q$. Nevertheless, other physical situations may eventually demand a revision on quasi-set theory axioms, if someone intends to use it in the quantum realm for the purpose of a clear discussion about non-individuality. I use this opportunity to suggest another way to cope with identity in quantum theories. (shrink)

The aim of this thesis is to propose a deflationary approach towards the ontological analysis of physical theories. Such an approach sustains that the development of ontologies for physical theories must be neutral relatively to the debate between realists and anti-realists in philosophy of physics. Mainly, our attention will be oriented towards what we called "quantum domain", which includes the non-relativistic Quantum Mechanics and variants of the Quantum Field Theory. This meta-ontological approach consists in an attempt to provide a methodology (...) for the development of specific ontologies for physical theories. With this aim we suggest the separation between physical phenomena and physical theories on one side, and physical theories and ontologies on the other side. This separation intends to endorse the idea that physical theories can provide all the informative contents required for the development of the ontologies associated with them. The result is a defense of the idea that physical theories can positively contribute for the constitution of the ontologies in physics. Additionally, we present a critical analysis of four different ontological approaches to QM and QFT. Each one of these interpretations deals with a different ontological category (tropes, events and processes). At the end of the thesis we will analyze the concepts of interaction and commutation in QFT in order to exemplify the main lines of the deflationary approach suggested here. (shrink)

Feynman's sum-over-histories formulation of quantum mechanics has been considered a useful calculational tool in which virtual Feynman histories entering into a coherent quantum superposition cannot be individually measured. Here we show that sequential weak values, inferred by consecutive weak measurements of projectors, allow direct experimental probing of individual virtual Feynman histories, thereby revealing the exact nature of quantum interference of coherently superposed histories. Because the total sum of sequential weak values of multitime projection operators for a complete set of orthogonal (...) quantum histories is unity, complete sets of weak values could be interpreted in agreement with the standard quantum mechanical picture. We also elucidate the relationship between sequential weak values of quantum histories with different coarse graining in time and establish the incompatibility of weak values for nonorthogonal quantum histories in history Hilbert space. Bridging theory and experiment, the presented results may enhance our understanding of both weak values and quantum histories. (shrink)

In this paper I investigate, within the framework of realistic interpretations of the wave function in nonrelativistic quantum mechanics, the mathematical and physical nature of the wave function. I argue against the view that mathematically the wave function is a two-component scalar field on configuration space. First, I review how this view makes quantum mechanics non- Galilei invariant and yields the wrong classical limit. Moreover, I argue that interpreting the wave function as a ray, in agreement many physicists, Galilei invariance (...) is preserved. In addition, I discuss how the wave function behaves more similarly to a gauge potential than to a field. Finally I show how this favors a nomological rather than an ontological view of the wave function. (shrink)

This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or toy model of quantum mechanics over sets (QM/sets). There have been several previous attempts to develop a quantum-like model with the base field of ℂ replaced by ℤ₂. Since there are no inner products on vector spaces over finite fields, the problem is to define the Dirac brackets and the probability calculus. The previous attempts (...) all required the brackets to take values in ℤ₂. But the usual QM brackets <ψ|ϕ> give the "overlap" between states ψ and ϕ, so for subsets S,T⊆U, the natural definition is <S|T>=|S∩T| (taking values in the natural numbers). This allows QM/sets to be developed with a full probability calculus that turns out to be a non-commutative extension of classical Laplace-Boole finite probability theory. The pedagogical model is illustrated by giving simple treatments of the indeterminacy principle, the double-slit experiment, Bell's Theorem, and identical particles in QM/Sets. A more technical appendix explains the mathematics behind carrying some vector space structures between QM over ℂ and QM/Sets over ℤ₂. (shrink)

The paper is replaced by a new version (12-2019): DOI: 10.5281/zenodo.3572846 -/- Physical phenomena emerge from the quantum fields everywhere in space. However, not only the phenomena emerge from the quantum fields, the law of the conservation of energy must have its origin from the same spatial structure. This paper describes the relations between the main law of physics and the mathematical structure of the “aggregated” quantum fields.

Instead of postulated fixed structures and abstract principles of usual positivistic science, the unreduced diversity of living world reality is consistently derived as dynamically emerging results of unreduced interaction process development, starting from its simplest configuration of two coupled homogeneous protofields. The dynamically multivalued, or complex and intrinsically chaotic, nature of these real interaction results extends dramatically the artificially reduced, dynamically single-valued projection of standard theory and solves its stagnating old and accumulating new problems, “mysteries” and “paradoxes” within the unified (...) and causally complete picture of intrinsically evolving, dynamically complex reality. The permanently unfolding complexity progress thus revealed is fundamentally unlimited and does not need to stop at the directly observed diversity of usual matter complexity. The exciting, but rigorously substantiated and objectively inevitable prospects of further civilisation complexity development towards its superior levels of genuine sustainability and global Noosphere are outlined, with practically important conclusions for today’s critical problem solution. (shrink)

In this paper I present the common structure of quantum theories with a primitive ontology, and discuss in what sense the classical world emerges from quantum theories as understood in this framework. In addition, I argue that the primitive ontology approach is better at answering this question than the rival wave function ontology approach or any other approach in which the classical world is nonreductively ‘emergent:’ even if the classical limit within this framework needs to be fully developed, the difficulties (...) are technical rather than conceptual, while this is not true for the alternatives. (shrink)

The aim of this paper is to summarize a particular approach of doing metaphysics through physics - the primitive ontology approach. The idea is that any fundamental physical theory has a well-defined architecture, to the foundation of which there is the primitive ontology, which represents matter. According to the framework provided by this approach when applied to quantum mechanics, the wave function is not suitable to represent matter. Rather, the wave function has a nomological character, given that its role in (...) the theory is to implement the law of evolution for the primitive ontology. (shrink)

It has been argued that the transition from classical to quantum mechanics is an example of a Kuhnian scientific revolution, in which there is a shift from the simple, intuitive, straightforward classical paradigm, to the quantum, convoluted, counterintuitive, amazing new quantum paradigm. In this paper, after having clarified what these quantum paradigms are supposed to be, I analyze whether they constitute a radical departure from the classical paradigm. Contrary to what is commonly maintained, I argue that, in addition to radical (...) quantum paradigms, there are also legitimate ways of understanding the quantum world that do not require any substantial change to the classical paradigm. (shrink)

Is the quantum state part of the furniture of the world? Einstein found such a position indigestible, but here I present a different understanding of the wavefunction that is easy to stomach. First, I develop the idea that the wavefunction is nomological in nature, showing how the quantum It or Bit debate gets subsumed by the corresponding It or Bit debate about laws of nature. Second, I motivate the nomological view by casting quantum mechanics in a “classical” formalism (Hamilton–Jacobi theory) (...) and classical mechanics in a “quantum” formalism (Koopman–von Neumann theory) and then comparing and contrasting classical and quantum wave functions. I argue that Humeans about laws can treat classical and quantum wave functions on a par and that doing so yields many benefits. (shrink)

We review a recent approach to the foundations of quantum mechanics inspired by quantum information theory. The approach is based on a general framework, which allows one to address a large class of physical theories which share basic information-theoretic features. We first illustrate two very primitive features, expressed by the axioms of causality and purity-preservation, which are satisfied by both classical and quantum theory. We then discuss the axiom of purification, which expresses a strong version of the Conservation of Information (...) and captures the core of a vast number of protocols in quantum information. Purification is a highly non-classical feature and leads directly to the emergence of entanglement at the purely conceptual level, without any reference to the superposition principle. Supplemented by a few additional requirements, satisfied by classical and quantum theory, it provides a complete axiomatic characterization of quantum theory for finite dimensional systems. (shrink)

It is an experimental fact that \ -decays produce in a cloud chamber at most one track and that this track points in a random direction. This seems to contradict the description of decay in Quantum Mechanics: according to Gamow a spherical wave is produced and moves radially according to Schrödinger’s equation. It is as if the interaction with the supersaturated vapor turned the wave into a particle. The aim of this note is to place this effect in the context (...) of Schrödinger’s Quantum Mechanics. We shall see that the properties of the initial wave function suggest the introduction of a semiclassical formalism in which the \ -wave can be described as a collection of semiclassical wavelets; each of them interacts with an atom and forms an entangled state. The interaction can be regarded as a semiclassical inelastic scattering event. The measurement selects the wave function of one of the ions, with a probability given by Born’s rule. This ion interacts with the atoms nearby leading to the formation of a droplet. One can reasonably assume that also the wavelet entangled with the selected ion has probability one to remain as part of the description of the system. The measurement process is therefore represented by a unitary operator. The wavelet remains sharply localized on a classical path \ It is still a probability wave: it determines the probability that another atom be ionized. This probability is essentially zero unless the atom lies on \ . This gives the visible track. (shrink)

The primary quantum mechanical equation of motion entails that measurements typically do not have determinate outcomes, but result in superpositions of all possible outcomes. Dynamical collapse theories (e.g. GRW) supplement this equation with a stochastic Gaussian collapse function, intended to collapse the superposition of outcomes into one outcome. But the Gaussian collapses are imperfect in a way that leaves the superpositions intact. This is the tails problem. There are several ways of making this problem more precise. But many authors dismiss (...) the problem without considering the more severe formulations. Here I distinguish four distinct tails problems. The first (bare tails problem) and second (structured tails problem) exist in the literature. I argue that while the first is a pseudo-problem, the second has not been adequately addressed. The third (multiverse tails problem) reformulates the second to account for recently discovered dynamical consequences of collapse. Finally the fourth (tails problem dilemma) shows that solving the third by replacing the Gaussian with a non-Gaussian collapse function introduces new conflict with relativity theory. (shrink)

In the present article, I propose to give a positive characterization of ontological emergence from a relational perspective that, in opposition both to atomism and to holism, defends that the existence-conditions, the identity and the behavior or causal role of any emergent entity are to be conceived, and explained, as constructed by diverse systems of qualitatively transformative relations. I argue that from this relational perspective, the notion of emergence can be seen as ontologically and epistemologically coherent and significant. Finally, I (...) try to show in what sense, and to what extent, the Nonlinear Quantum Physics, as developed by Croca and his team, expresses such a relational and emergentist view of physical reality. (shrink)

A brief account of epistemological models that try to unfold the intertheoretic context of theory change is proposed. It is stated that all of them has a host of drawbacks, the most salient one being the lack of adequate description of the research traditions interaction process. The epistemological model of mature theory change, eliminating the drawback, is contemplated and illustrated.

Book Review of: Dow We Really Understand Quantum Mechanics? by Franck Laloe.

There has been a long-standing and sometimes passionate debate between physicists over whether a dynamical framework for quantum systems should incorporate not completely positive (NCP) maps in addition to completely positive (CP) maps. Despite the reasonableness of the arguments for complete positivity, we argue that NCP maps should be allowed, with a qualification: these should be understood, not as reflecting ‘not completely positive’ evolution, but as linear extensions, to a system’s entire state space, of CP maps that are only partially (...) defined. Beyond the domain of definition of a partial-CP map, we argue, much may be permitted. (shrink)

This paper puts forward the problem of singularity – one of the most important issues in contemporary cosmology. Firstly, the history of “singularity” concept and basis of Penrose’s and Hawking’s theorem of singularity are discussed. Secondly, the problem of singularity is presented as a genesis of search of quantum theories of the beginning of the Universe, in which the concept of singularity is not present. One sophisticated concept of Hartle and Hawking is presented, in particular the authors’ methodology is described. (...) The paper shows many possible philosophical problems which are connected with quantum cosmology. (shrink)

Von Neumann in 1932 was the first to outline the possible non-existence of dispersion free ensembles in quantum mechanics, and he used this basic evidence to give a preliminary proof on incompatibility between quantum mechanics and local hidden variables theory. In the present paper, we give a detailed theoretical elaboration on the manner in which such a fundamental subject could be explored at perceptive and cognitive levels in humans. We also discuss a general design of the experiment that we have (...) in progress so to give direct indications to other researchers engaged in such field. (shrink)

The phase φ of any wave is determined by the ratio x/λ consisting of the distance x propagated by the wave and its wavelength λ. Hence, the dependence of φ on λ constitutes an analogue system for the mathematical operation of division, that is to obtain the hyperbolic function f(ξ)≡1/ξ. We take advantage of this observation to decompose integers into primes and implement this approach towards factorization of numbers in a multi-path Michelson interferometer. This work is part of a larger (...) program geared towards unraveling the connections between quantum mechanics and number theory. We briefly summarize this aspect. (shrink)

A non-classical, non-quantum theory, or NCQ, is any fully consistent theory that differs fundamentally from both the corresponding classical and quantum theories, while exhibiting certain features common to both. Such theories are of interest for two primary reasons. Firstly, NCQs arise prominently in semi-classical approximation schemes. Their formal study may yield improved approximation techniques in the near-classical regime. More importantly for the purposes of this note, it may be possible for NCQs to reproduce quantum results over experimentally tested regimes while (...) having a well defined classical limit, and hence are viable alternative theories. We illustrate an NCQ by considering an explicit class of NCQ mechanics. Here this class will be arrived at via a natural generalization of classical mechanics formulated in terms of a probability density functional. (shrink)

With the purpose of introducing a useful tool for researches concerning foundations of quantum mechanics and applications to quantum technologies, here we address three quantumness quantifiers for bipartite optical systems: one is based on sub-shot-noise correlations, one is related to antibunching and one springs from entanglement determination. The specific cases of parametric downconversion seeded by thermal, coherent and squeezed states are discussed in detail.

A cura di Ignazio Licata, Ammar J. Sakaji Jeffrey A. Barrett, Enrico Celeghini, Leonardo Chiatti, Maurizio Consoli, Davide Fiscaletti, Ervin Goldfain, Annick Lesne, Maria Paola Lombardo, Mohammad Mehrafarin, Ronald Mirman, Ulrich Mohrhoff, Renato Nobili, Farrin Payandeh, Eliano Pessa, L.I Petrova, Erasmo Recami, Giovanni Salesi, Francesco Maria Scarpa, Mohammad Vahid Takook, Giuseppe Vitiello This volume comes out from an informal discussion between friends and colleagues on the answer:what topic do you think as fundamental in theoretical physics nowadays? Obviously wereceived different answers (...) according to the disposition and the different research areas, and answersin superposition state too. And yet some attractors have emerged pointing out the keys forthe Physicists conception of Nature, all of them converging towards a group of stronglyinterconnectedproblems. Let's see them one by one:. The concept of particle identity in Quantum Mechanics (QM) and Quantum Field Theory (QFT);. The relationship between QM and QFT, in particular the non -local aspects in Field Theory andthe problem of non-perturbative solutions;. The local/global problem in the relationship between particle physics and cosmology;. The role of Renormalization group in describing the meso and macroscopic emergent behaviour;. The possible extension of Poincaré symmetry group and Quantum cosmology;. Higgs "mechanism" and the origin of mass. (shrink)

Quantum theories constructed on the noncommutative spacetime called the Groenewold–Moyal plane exhibit many interesting properties such as Lorentz and CPT noninvariance, causality violation and twisted statistics. We show that such violations lead to many striking features that may be tested experimentally. These theories predict Pauli forbidden transitions due to twisted statistics, anisotropies in the cosmic microwave background radiation due to correlations of observables in spacelike regions and Lorentz and CPT violations in scattering amplitudes.

Quantum information theory has given rise to a renewed interest in, and a new perspective on, the old issue of understanding the ways in which quantum mechanics differs from classical mechanics. The task of distinguishing between quantum and classical theory is facilitated by neutral frameworks that embrace both classical and quantum theory. In this paper, I discuss two approaches to this endeavour, the algebraic approach, and the convex set approach, with an eye to the strengths of each, and the relations (...) between the two. I end with a discussion of one particular model, the toy theory devised by Rob Spekkens, which, with minor modifications, fits neatly within the convex sets framework, and which displays in an elegant manner some of the similarities and differences between classical and quantum theories. The conclusion suggested by this investigation is that Schrödinger was right to find the essential difference between classical and quantum theory in their handling of composite systems, though Schrödinger's contention that it is entanglement that is the distinctive feature of quantum mechanics needs to be modified. (shrink)

We maximally extend the quantum‐mechanical results of Muller and Saunders ( 2008 ) establishing the ‘weak discernibility’ of an arbitrary number of similar fermions in finite‐dimensional Hilbert spaces. This confutes the currently dominant view that ( A ) the quantum‐mechanical description of similar particles conflicts with Leibniz’s Principle of the Identity of Indiscernibles (PII); and that ( B ) the only way to save PII is by adopting some heavy metaphysical notion such as Scotusian haecceitas or Adamsian primitive thisness. We (...) take sides with Muller and Saunders ( 2008 ) against this currently dominant view, which has been expounded and defended by many. *Received July 2008; revised May 2009. †To contact the authors, please write to: F. A. Muller, Faculty of Philosophy, Erasmus University Rotterdam, Burg. Oudlaan 50, H5–16, 3062 PA Rotterdam, The Netherlands; e‐mail: f.a.muller@fwb.eur.nl , and Institute for the History and Foundations of Science, Utrecht University, Budapestlaan 6, IGG–3.08, 3584 CD Utrecht, The Netherlands; e‐mail: f.a.muller@uu.nl . M. P. Seevinck, Institute for the History and Foundations of Science, Utrecht University, Budapestlaan 6, IGG–3.08, 3584 CD Utrecht, The Netherlands; e‐mail: m.p.seevinck@uu.nl. (shrink)

Rudyard Kipling, the famous english author of « The Jungle Book », born in India, wrote one day these words: « Oh, East is East and West is West, and never the twain shall meet ». In my paper I show that Kipling was not completely right. I try to show the common ground between buddhist philosophy and quantum physics. There is a surprising parallelism between the philosophical concept of reality articulated by Nagarjuna and the physical concept of reality implied (...) by quantum physics. For neither is there a fundamental core to reality, rather reality consists of systems of interacting objects. Such concepts of reality cannot be reconciled with the substantial, subjective, holistic or instrumentalistic concepts of reality which underlie modern modes of thought. (shrink)

Gregor Schiemann führt allgemeinverständlich in das Denken dieses Physikers ein. Thema sind die Erfahrungen und Überlegungen, die Heisenberg zu seinen theoretischen Erkenntnissen geführt haben, die wesentlichen Inhalte dieser Erkenntnisse sowie die Konsequenzen, die er daraus für die Geschichte der Physik und das wissenschaftliche Weltbild gezogen hat. Heisenbergs Vorstellungswelt durchzieht durch ein Spannungsverhältnis, das heute noch das Denken vieler Wissenschaftlerinnen und Wissenschaftler bewegt. Er ist um ein umfassendes Verständnis der Naturprozesse bemüht, zugleich aber von der Berechenbarkeit und Beherrschbarkeit von Phänomenen auch (...) dann schon fasziniert, wenn die zugrunde liegenden Prozesse erst teilweise verstanden sind. Aus der Geschichte der Physik zieht er die wirkungsreiche Lehre, daß sich die naturwissenschaftliche Erkenntnis nicht kontinuierlich, sondern sprunghaft in Form von Revolutionen entwickelt. Die Reichweite des physikalischen Wissens begrenzt er in einer Schichtentheorie der Welt, nach der die komplexen Phänomene des Lebens nicht allein durch die Wechselwirkungen zwischen ihren Bestandteilen erklärt werden können. Der zunehmenden Technisierung der Welt steht Heisenberg kritisch gegenüber. Seiner Zeit weit voraus, glaubt er, daß die Technisierung der Welt eine epochal neue Stufe erreicht habe, in der der Mensch „nur noch sich selbst“ gegenüberstehe. (shrink)

In this paper I outline my propensiton version of quantum theory (PQT). PQT is a fully micro-realistic version of quantum theory that provides us with a very natural possible solution to the fundamental wave/particle problem, and is free of the severe defects of orthodox quantum theory (OQT) as a result. PQT makes sense of the quantum world. PQT recovers all the empirical success of OQT and is, furthermore, empirically testable (although not as yet tested). I argue that Einstein almost put (...) forward this version of quantum theory in 1916/17 in his papers on spontaneous and induced radiative transitions, but retreated from doing so because he disliked the probabilistic character of the idea. Subsequently, the idea was overlooked because debates about quantum theory polarised into the Bohr/Heisenberg camp, which argued for the abandonment of realism and determinism, and the Einstein/Schrödinger camp, which argued for the retention of realism and determinism, no one, as a result, pursuing the most obvious option of retaining realism but abandoning determinism. It is this third, overlooked option that leads to PQT. PQT has implications for quantum field theory, the standard model, string theory, and cosmology. The really important point, however, is that it is experimentally testable. I indicate two experiments in principle capable of deciding between PQT and OQT. (shrink)

We review the problem of finding a general framework within which one can construct quantum theories of non-standard models for space, or space-time. The starting point is the observation that entities of this type can typically be regarded as objects in a category whose arrows are structure-preserving maps. This motivates investigating the general problem of quantising a system whose ‘configuration space’ (or history-theory analogue) is the set of objects Ob(Q) in a category Q. We develop a scheme based on constructing (...) an analogue of the group that is used in the canonical quantisation of a system whose configuration space is a manifold Q ≃ G/H, where G and H are Lie groups. In particular, we choose as the analogue of G the monoid of “arrow fields” on Q. Physically, this means that an arrow between two objects in the category is viewed as an analogue of momentum. After finding the ‘category quantisation monoid’, we show how suitable representations can be constructed using a bundle (or, more precisely, presheaf) of Hilbert spaces over Ob(Q). For the example of a category of finite sets, we construct an explicit representation structure of this type. (shrink)

The arguments that are often put forward to justify the singular importance given to completely positive maps over more generic maps in describing open quantum evolution are studied. We find that these do not appear convincing on closer examination. Positive as well as not positive maps are good candidates for describing open quantum evolution.

In the early 1960s of the 20th century de Broglie was able to explain the cosmological observable red shift, without ad hoc assumptions. Starting from basic quantum considerations he developed his tired light model for the photon. This model explains in a single and beautiful causal way the cosmological redshift without need of assuming the Big Bang and consequently a beginning for the universe. Evidence coming from Earth sciences seems also to confirm these ideas and furthermore concrete proposal of laboratorial (...) scale experiments that can test the model are reviewed. (shrink)

The theoretical description of particle decay by a single particle theory requires the use of a probability density in time that is not present in conventional theories. The problem of single particle decay is consistently described here within the context of a single particle, relativistic dynamical theory. We derive experimentally testable differences between the standard model and Relativistic Dynamics for a two-state system: the neutral K-meson (K 0) system. We show that the estimate of mass difference between the two states (...) is theory dependent. (shrink)

In this paper, a survey is made of some of the contributions to the interpretation of Hartle and Hawking’s theory of the wave function of the universe and its beginning. It is argued that there are considerable difficulties with the interpretation of the theory, but that there is at least one interpretation hitherto not found in the literature which survives existing philosophical objections.

The spectral fluctuations of quantum (or wave) systems with a chaotic classical (or ray) limit are mostly universal and faithful to random-matrix theory. Taking up ideas of Pechukas and Yukawa we show that equilibrium statistical mechanics for the fictitious gas of particles associated with the parametric motion of levels yields spectral fluctuations of the random-matrix type. Previously known clues to that goal are an appropriate equilibrium ensemble and a certain ergodicity of level dynamics. We here complete the reasoning by establishing (...) a power law for the ħ dependence of the mean parametric separation of avoided level crossings. Due to that law universal spectral fluctuations emerge as average behavior of a family of quantum dynamics drawn from a control parameter interval which becomes vanishingly small in the classical limit; the family thus corresponds to a single classical system. We also argue that classically integrable dynamics cannot produce universal spectral fluctuations since their level dynamics resembles a nearly ideal Pechukas–Yukawa gas. (shrink)

The ’microcausality’ condition in quantum field theory is typically presented and justified on the basis of general principles of physical causality. I explore in detail a number of alternative causal interpretations of this condition. I conclude that none is fully satisfactory, independent of further and controversial assumptions about the object and scope of quantum field theories. In particular the stronger causalreadings require a fully reductionist and fundamentalist attitude to quantum field theory. I argue, in a deflationary spirit, for a reading (...) of the ‘microcausality’ condition as merely a boundary condition, inspired by Relativity, that different possible formulations of quantum field theory must obey. (shrink)

The experimental confirmation of nonlocality has renewed interest in Bohm's quantum potential. The construction of quantum potentials for relativistic systems has encountered difficulties which do not arise in a parametrized formulation of relativistic quantum mechanics known as Relativistic Dynamics. The purpose of this paper is to show how to construct a quantum potential in the relativistic domain by deriving a relativistically invariant quantum potential using Relativistic Dynamics. The formalism is applied to three relativistic scalar particle models: a single particle interacting (...) with a scalar potential; N particles interacting with a scalar potential; and a single particle interacting with an electromagnetic 4-vector potential. (shrink)

In a recent essay, Quentin Smith revisits a question of philosophical cosmology. Why does the universe exist? This is one way of asking the existence question EQ. Smith notes that all theistic philosophical cosmologists have answered this question in terms of God’s creative choice. Smith favors an “atheistic” philosophical answer: “The universe exists because it has an unconditional probability of existing based on a fundamental law of nature.” He further declares: “This law of nature... is inconsistent with theism and implies (...) that God does not exist.” The structure of Smith's reasoning in defense of these claims is the following: The answer to EQ of theistic philosophical cosmologists is logically inconsistent with the answer of atheistic philosophical cosmologists. Therefore, theistic and atheistic philosophical cosmologies are logically inconsistent with each other. The atheistic answer to EQ is a complete answer to EQ. Therefore, theism is demonstrably false. I shall argue that Smith’s reasoning in defense of is not sound. From that, it follows that is not a proven truth. Assumption is controversial, and in the present context question-begging. It presupposes that materialism is true. Therefore, is not a proven truth. (shrink)

Recent authors have raised objections to the counterfactual interpretation of the Aharonov-Bergmann-Lebowitz rule of time-symmetrised quantum theory. I distinguish between two different readings of the ABL rule, counterfactual and non-counterfactual, and confirm that TSQT advocate L. Vaidman is employing the counterfactual reading to which these authors object. Vaidman has responded to the objections by proposing a new kind of time-symmetrised counterfactual, which he has defined in two different ways. It is argued that neither definition succeeds in overcoming the objections, except (...) in a limited special case previously noted by Cohen and Hiley. In addition, a connection is made between TSQT and Price's concept of 'advanced action', which further supports the special case discussed. (shrink)

Recent work in parametrized relativistic quantum theory (PRQT) has shown that oscillations between mass states are predicted by an alternative formulation of relativistic quantum theory that uses an invariant evolution parameter. A PRQT model of flavor transitions is compared to the standard model. The resulting PRQT expression for the probability of survival of an incident neutrino differs significantly from the standard neutrino oscillation model. Neutrino oscillation measurements provide an experimental testing ground for two theories that are based on fundamentally different (...) concepts of temporal evolution. (shrink)